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Modélisation du comportement extrême de processus spatio-temporels. Applications en océanographie et météorologie.

Abstract : In this thesis, the extremes of an important oceanographic variable for application will be studied: the significant wave height. This quantity is observed precisely thanks to remote sensing with the satellites. However, this data source produce complex data set with data irregularly spaced in space and time. This issue is central for studding extreme values, since few models are suited to such data. Two models are described in this document. First, we introduce an interpolation model, based on the estimation of displacements sea-states structures, thanks to particle filters. Then, an estimation of the covariance structure of the displaced field is applied to obtain and interpolation scheme. This technique leads to an improvement of usual approaches, but is insufficient to cope with extremes. Secondly, we develop a procedure to model the threshold exeedances for a process observed at irregular time steps or with missing observations. We propose a model based on methods from multivariate threshold exceedances and from extremes of stochastic processes, together with an estimation procedure inspired by composite likelihood techniques. Then, we show both the consistency of the estimators and the practical behaviour with simulations. Last, we use real datasets of significant wave height and see that taking into account every excess leads to an improvement in the estimation of return level and in describing the lengths of extreme events.
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Contributor : Nicolas Raillard Connect in order to contact the contributor
Submitted on : Wednesday, January 4, 2012 - 2:19:54 PM
Last modification on : Friday, May 20, 2022 - 9:04:46 AM
Long-term archiving on: : Thursday, April 5, 2012 - 2:25:58 AM


  • HAL Id : tel-00656468, version 1


Nicolas Raillard. Modélisation du comportement extrême de processus spatio-temporels. Applications en océanographie et météorologie.. Statistiques [math.ST]. Université Rennes 1, 2011. Français. ⟨tel-00656468⟩



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